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NumericalAlgebraicGeometry :: randomSd(List)

randomSd(List) -- a random homogeneous system of polynomial equations

Synopsis

Description

Generates a system of homogeneous polynomials Ti such that deg(Ti) = di. The system is normalized, so that it is on the unit sphere in the Bombieri-Weyl norm.

i1 : T = randomSd {2,3}

                                2                                      
o1 = {(- .169102 - .182043*ii)x1  + (- .0408283 - .395475*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                           
     .265861 - .226302*ii)x2  + (.441176 - .420645*ii)x1*x3 + (.200512 -
     ------------------------------------------------------------------------
                                                  2              
     .203395*ii)x2*x3 + (- .296613 + .136984*ii)x3 , (- .114981 +
     ------------------------------------------------------------------------
                  3                            2                 
     .193703*ii)x1  + (.431031 - .0669649*ii)x1 x2 + (- .189662 -
     ------------------------------------------------------------------------
                     2                            3               
     .305648*ii)x1*x2  + (- .02399 + .134492*ii)x2  + (- .348505 +
     ------------------------------------------------------------------------
                  2                                                  
     .183848*ii)x1 x3 + (- .115061 + .270642*ii)x1*x2*x3 + (.272137 -
     ------------------------------------------------------------------------
                2                                  2              
     .3945*ii)x2 x3 + (- .078749 + .283242*ii)x1*x3  + (.0959844 -
     ------------------------------------------------------------------------
                     2                              3
     .165131*ii)x2*x3  + (- .0447168 - .205809*ii)x3 }

o1 : List
i2 : (S,solsS) = goodInitialPair T;
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{.230223-.458901*ii, -.565231+.460002*ii, .226576+.392406*ii}}

o3 : List

See also